This chapter applies the Fundamental Efficiency Theorem to a central problem in basic Stirling engine design, that of identifying optimal engine geometry. This problem was treated in Chapter 7 for highly idealized engines having theoretical mechanisms, heat exchangers, etc. to produce cycles consisting of four distinct uniform thermodynamic processes. The results in Chapter 7 clearly showed the influence that the type of thermodynamic processes and the level of mechanism effectiveness have on optimum compression ratio and engine output potential.

In this chapter, a more realistic mechanical model of the Stirling engine is employed. It faithfully reflects practical and typical mechanical motions for the piston and displacer. In this setting, optimum values of two parameters are identified which yield maximum brake work output. In the interest of mathematical tractability, the thermal model used here is still highly idealized in that limitations in heat transfer are not considered. Accordingly, it yields best-case results, but allowing for this in a rational way when applying the optima in practical situations can provide an improved guide for first-order design of new engines.

THE GAMMA ENGINE

The analysis is limited here to a particular type of Stirling known as the gamma or split-cylinder. Illustrated in Figure 10.1, the split-cylinder is the simplest of the three main Stirling engine configurations.